Commerce (English Medium) कक्षा १२ - CBSE Important Questions

Write the sum of the order and the degree of the following differential equation:

`d/(dx) (dy/dx)` = 5

Find the general solution of the following differential equation:

`x (dy)/(dx) = y - xsin(y/x)`

Find the particular solution of the following differential equation, given that y = 0 when x = `pi/4`.

`(dy)/(dx) + ycotx = 2/(1 + sinx)`

If m and n, respectively, are the order and the degree of the differential equation `d/(dx) [((dy)/(dx))]^4` = 0, then m + n = ______.

The general solution of the differential equation y dx – x dy = 0 is ______.

Solve the differential equation: y dx + (x – y²)dy = 0

Solve the differential equation: xdy – ydx = `sqrt(x^2 + y^2)dx`

Solve the following differential equation: (y – sin²x)dx + tanx dy = 0

Find the general solution of the differential equation: (x³ + y³)dy = x²ydx

Find the general solution of the differential equation:

`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`

The order and the degree of the differential equation `(1 + 3 dy/dx)^2 = 4 (d^3y)/(dx^3)` respectively are ______.

The general solution of the differential equation ydx – xdy = 0; (Given x, y > 0), is of the form

(Where 'c' is an arbitrary positive constant of integration)

If `(a + bx)e^(y/x)` = x then prove that `x(d^2y)/(dx^2) = (a/(a + bx))^2`.

The degree of the differential equation `[1 + (dy/dx)^2]^3 = ((d^2y)/(dx^2))^2` is ______.

If `veca ` and `vecb` are two unit vectors such that `veca+vecb` is also a  unit vector, then find the angle between `veca` and `vecb`

If a unit vector `veca` makes angles `pi/3` with `hati,pi/4` with `hatj` and acute angles θ with ` hatk,` then find the value of θ.

If `veca and vecb` are two vectors such that `|veca+vecb|=|veca|,` then prove that vector `2veca+vecb` is perpendicular to vector `vecb`

Write the number of vectors of unit length perpendicular to both the vectors `veca=2hati+hatj+2hatk and vecb=hatj+hatk`

Write the position vector of the point which divides the join of points with position vectors `3veca-2vecb and 2veca+3vecb` in the ratio 2 : 1.

The two adjacent sides of a parallelogram are `2hati-4hatj-5hatk and 2 hati+2hatj+3hatj` . Find the two unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram.